Visualizing nonclassical effects in phase space

Abstract

Nonclassicality filters provide a universal method to visualize the nonclassicality of arbitrary quantum states of light through negativities of a regularized Glauber-Sudarshan P function, also denoted as nonclassicality quasiprobability. Such filters are introduced and analyzed for optimizing the experimental certification of nonclassical effects. An analytic filter is constructed which preserves the full information on the quantum state. For balanced homodyne detection, the number of data points is analyzed to get the negativities of the nonclassicality quasiprobability with high statistical significance. The method is applied to different scenarios, such as phase randomized squeezed vacuum states, single-photon-added thermal states, and heralded state engineering with array detectors. The generalization to visualize quantum correlations of multimode radiation fields is also considered.

Preparation of arbitrary quantum states with regular P functions

“…It was shown in Ref. [35] and later confirmed in experiment [23], that a larger value of q leads to a clearly improved statistical significance of the negativity of the regularized P function, P w , sampled from a fixed amount of data in balanced homodyne detection. In fact, the significance is maximal in the limit q → ∞.…”

Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion

“…where L (k) n (x) are the generalized Laguerre polynomials. Using a radial symmetric filter function [102], Ω w (β) ≡ Ω w (|β|) with x = |x|e iϕx for α and β, then P Ω,nm (α) may be rewritten as…”

“…This relation holds true for all radial symmetric filters Ω w (|β|). We will use the filter [102] Ω w (|β|) = 2 π arccos |β| 2w − |β|…”

Quantum correlations in composite systems

“…which includes the width parameter 0 < w ≤ ∞. More general classes of filters can be additionally found in [43]. This regularization approach has been used, for example, to experimentally uncover the negative quasiprobability of a squeezed state [44,45,46], which would be impossible with the frequently applied Wigner function.…”